6.6 Polynomials with Special Products

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6.6 Polynomials with Special Products

Polynomial Vocabulary Standard Form – Largest exponent to smallest exponent Lead Coefficient – Coefficient of term with largest exponent Degree – Largest exponent (number of factors (P.4))

Addition/Subtraction (answer in standard form)

Examples: (9x3 – 2x + 1) + (5x2 + 12x -4) =

Multiplication (Distribute)

Multiplying Polynomials : Horizontally (x – 3)(3x2 – 2x – 4)= 3x3 – 2x2 – 4x – 9x2 + 6x + 12= 3x3 – 11x2 + 2x + 12

There are formulas (shortcuts) that work for certain polynomial multiplication problems. (a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 – 2ab + b2 (a - b)(a + b) = a2 - b2 Being able to use these formulas will help you in the future when you have to factor. If you do not remember the formulas, you can always multiply using distributive.

Multiplying Conjugates (Difference of Two Squares)

Multiply each:

Rewrite each of the following as a polynomial in standard form: (You have seven minutes)